Find the area of the triangle whose vertices are `A(3,-1,2),\ B(1,-1,-3)a n d\ C(4,-3,1)dot`

Explanation

To find the area of the triangle with vertices \( A(3, -1, 2) \), \( B(1, -1, -3) \), and \( C(4, -3, 1) \), we can use the formula for the area of a triangle given by the vertices in three-dimensional space. The area \( A \) can be calculated using the formula:

\[ A = \frac{1}{2} \| \vec{AB} \times \vec{AC} \| \]

where \( \vec{AB} \) and \( \vec{AC} \) are the vectors formed by the points \( A \), \( B \), and \( C \).

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